Preconditioning for Allen-Cahn variational inequalities with non-local constraints. (English) Zbl 1250.49007
Summary: The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. The heart of this method is the solution of linear systems in saddle point form. In this paper, we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach.
MSC:
| 49J40 | Variational inequalities |
| 49J35 | Existence of solutions for minimax problems |
| 49M15 | Newton-type methods |
Keywords:
PDE-constrained optimization; Allen-Cahn model; Newton method; saddle point systems; preconditioning; Krylov subspace solverReferences:
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